CN104574319B - The blood vessel Enhancement Method and system of a kind of lung CT image - Google Patents
The blood vessel Enhancement Method and system of a kind of lung CT image Download PDFInfo
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- 210000004204 blood vessel Anatomy 0.000 title claims abstract description 60
- 238000000034 method Methods 0.000 title claims abstract description 29
- 210000004072 lung Anatomy 0.000 title claims abstract description 24
- 239000013598 vector Substances 0.000 claims abstract description 60
- 238000009792 diffusion process Methods 0.000 claims abstract description 16
- 230000001186 cumulative effect Effects 0.000 claims description 14
- 238000000354 decomposition reaction Methods 0.000 claims description 7
- 238000005728 strengthening Methods 0.000 claims description 7
- 239000011159 matrix material Substances 0.000 claims description 5
- 230000008569 process Effects 0.000 claims description 3
- 235000013399 edible fruits Nutrition 0.000 claims 1
- 230000002708 enhancing effect Effects 0.000 abstract description 11
- 230000002792 vascular Effects 0.000 abstract description 8
- 230000000694 effects Effects 0.000 abstract description 4
- 230000001629 suppression Effects 0.000 abstract description 3
- 230000006870 function Effects 0.000 description 15
- 210000004369 blood Anatomy 0.000 description 3
- 239000008280 blood Substances 0.000 description 3
- 230000006872 improvement Effects 0.000 description 2
- 230000004044 response Effects 0.000 description 2
- 206010028980 Neoplasm Diseases 0.000 description 1
- 208000008469 Peptic Ulcer Diseases 0.000 description 1
- 230000008901 benefit Effects 0.000 description 1
- 210000000621 bronchi Anatomy 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 230000007850 degeneration Effects 0.000 description 1
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- 238000003745 diagnosis Methods 0.000 description 1
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- 238000003384 imaging method Methods 0.000 description 1
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Abstract
The invention belongs to image processing field, there is provided the blood vessel Enhancement Method and system of a kind of lung CT image.This method and system are that Vessel Enhancing Diffusion (VED) algorithm is improved, estimating after every bit belongs to the possibility of tubular structure, pass through rod Tensor Voting, characteristic point and characteristic vector are reconstructed, recycle spread function to carry out image enhaucament afterwards.Relative to VED algorithms, due to make use of the tensor direction of neighborhood, blood vessel trend to vascular wall has carried out rod Tensor Voting, so as to correct for the tensor direction around vascular wall and be reconstructed new tensor direction, diffusion of the blood vessel intensity along blood vessel tangent plane can be preferably reduced using the tensor direction of reconstruct, diffusion of the enhancing along vessel directions simultaneously, reach suppression noise, strengthen the effect of blood vessel feature, solve the presence of VED algorithms tubular structure edge feature direction it is mixed and disorderly caused by enhancing effect distortion the problem of.
Description
Technical field
The invention belongs to the blood vessel Enhancement Method and system of image processing field, more particularly to a kind of lung CT image.
Background technology
CT images are the scan images a part of to human body, can to imaging of tissue such as blood vessel, tumours, aid in doctor and
When select rational therapy method.For lung CT image, due to wherein there is the tissue of a large amount of tubular structures (such as bronchus, blood
Pipe etc.), in order to protrude these tubular structures, suppress ambient noise, help the diagnosis of PUD D, it is necessary to pass through image enhaucament skill
Art strengthens it.
Prior art proposes the blood vessel Enhancement Method of a variety of lung CT images.Wherein, based on Hai Sen (Hessian) matrix
Multiple dimensioned blood vessel enhancing algorithm be a conventional class method.Such method using Hessian matrixes characteristic value and feature to
Amount distinguishes blood vessel and background, and local geometric features are extracted using second dervative.In all multiple dimensioned blood based on Hessian matrixes
In pipe enhancing algorithm, Frangi algorithms consider All Eigenvalues and have made geometric interpretation to blood vessel detection, and this method can
To detect most blood vessels under different scale, obtain quite being widely applied.But, Frangi algorithms compare noise
Sensitivity, occurs a large amount of distributed noises after enhancing, further, since the algorithm only has response to linear structure, to other structures
There is inhibitory action, such as smaller response can be obtained at intersecting blood vessels, rupture of blood vessel phenomenon is caused.
Blood vessel enhanced diffustion (Vessel Enhancing Diffusion, VED) algorithm is calculated Frangi in terms of two
Method is improved.First, VED algorithms add smoothing factor in the blood vessel function of Frangi algorithms, reduce it
Influence to noise, so that smoothened continuous；Secondly, VED algorithms are spread to the tubular structure detected, and then more
Mend the blood vessel that Frangi algorithms detect and the defect being broken occur.
But, although VED algorithms solve the noise and breakage problem of Frangi algorithms appearance to a certain extent, but
It is that, due to the presence of noise, it is the same consistent with blood vessel trend that the dispersal direction of vascular wall is not as blood vessel middle part, but by
, there is the mixed and disorderly phenomenon of dispersal direction in the interference of ambient noise, and this mixed and disorderly dispersal direction causes blood vessel may be to blood vessel
Tangent plane direction is spread, and the blood vessel after diffusion is coarser than original blood vessel, is caused the enhanced effect distortion of blood vessel.
The content of the invention
It is an object of the invention to provide a kind of blood vessel Enhancement Method of lung CT image, it is intended to solves prior art proposition
VED algorithms due to the presence of noise, make its dispersal direction at vascular wall mixed and disorderly, cause asking for blood vessel enhancing effect distortion
Topic.
The present invention is achieved in that a kind of blood vessel Enhancement Method of lung CT image, the described method comprises the following steps：
The Hessian matrixes and its characteristic value and characteristic vector of every bit in image are calculated, and according to characteristic value and feature
Vector estimation every bit belongs to the possibility of tubular structure；
Using the minimum direction of the characteristic value of point of the possibility more than 0 as normal direction, 0 is more than to other possibilities in its neighborhood
Point carry out rod Tensor Voting, and according to voting results to each possibility be more than 0 point characteristic value and characteristic vector carry out
Reconstruct, direction is moved towards to determine that each possibility is more than the tubular structure of 0 point；
According to the characteristic vector of reconstruct, 0 point is more than using spread function to each possibility described in described image
Intensity is updated, untill update times reach maximum iteration.
Another object of the present invention is to provide a kind of blood vessel strengthening system of lung CT image, the system includes：
Computing module, Hessian matrixes and its characteristic value and characteristic vector for calculating every bit in image, and according to
Characteristic value and characteristic vector estimation every bit belong to the possibility of tubular structure；
Reconstructed module, for being more than the minimum direction of 0 characteristic value of point using possibility as normal direction, to other in neighborhood
Possibility be more than 0 point carry out rod Tensor Voting, and according to voting results to each possibility be more than 0 point characteristic value and spy
Levy vector to be reconstructed, direction is moved towards to determine that each possibility is more than the tubular structure of 0 point；
Module is spread, it is big to each possibility described in image using spread function for the characteristic vector according to reconstruct
It is updated in the intensity of 0 point, untill update times reach maximum iteration.
The blood vessel Enhancement Method and system of lung CT image proposed by the present invention are that VED algorithms are improved, and are being estimated
Count out every bit to belong to after the possibility of tubular structure, by rod Tensor Voting, characteristic value and characteristic vector are weighed
Structure, recycles spread function to carry out image enhaucament afterwards.Relative to VED algorithms, due to make use of the tensor direction of neighborhood, to blood
The blood vessel trend of tube wall has carried out rod Tensor Voting, so as to correct for the tensor direction around vascular wall and be reconstructed new tensor
Direction, diffusion of the blood vessel intensity along blood vessel tangent plane can be preferably reduced using the tensor direction of reconstruct, while strengthening along blood vessel
The diffusion in direction, reaches suppression noise, strengthens the effect of blood vessel feature, and the tubular structure edge for solving the presence of VED algorithms is special
Levy direction it is mixed and disorderly caused by enhancing effect distortion the problem of.
Brief description of the drawings
Fig. 1 is the flow chart of the blood vessel Enhancement Method of lung CT image provided in an embodiment of the present invention；
During Fig. 2 is the embodiment of the present invention, the detail flowchart that every bit belongs to the possibility of tubular structure is obtained；
During Fig. 3 is the embodiment of the present invention, the detail flowchart that characteristic value and characteristic vector are reconstructed；
Fig. 4 is the structure chart of the blood vessel strengthening system of lung CT image provided in an embodiment of the present invention；
Fig. 5 is the structure chart of computing module in Fig. 4；
Fig. 6 is the structure chart of reconstructed module in Fig. 4.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, it is right below in conjunction with drawings and Examples
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.
For solution VED algorithms are affected by noise and occur the mixed and disorderly phenomenon of diffusion at vascular wall, lung proposed by the present invention
The blood vessel Enhancement Method and system of portion's CT images are the improvement carried out to VED algorithms, belong to tubular structure estimating every bit
Possibility after, by rod Tensor Voting, characteristic value and characteristic vector are reconstructed, afterwards recycle spread function enter
Row image enhaucament.
Fig. 1 shows the flow of the blood vessel Enhancement Method of lung CT image provided in an embodiment of the present invention, including following step
Suddenly：
S1：The Hessian matrixes and its characteristic value and characteristic vector of every bit in image are calculated, and according to characteristic value and spy
Levy the possibility that vector estimation every bit belongs to tubular structure.
Further, as shown in Fig. 2 step S1 may include following steps again：
S11：Image is carried out using multiple dimensioned Gaussian function smooth.
Assuming that G (x, y, z；Be σ) three-dimensional Gaussian function that yardstick is σ, then sharpening result Is of the image I (x, y, z) under yardstick σσ
(x, y, z) is expressed as：Wherein,
S12：Under each yardstick, the Hessian matrixes of every bit in image are calculated according to sharpening result.
Assuming that under yardstick σ, the Hessian matrixes at image midpoint (x, y, z) place are Hσ(x, y, z), then it is expressed as：
S13：Eigenvalues Decomposition is carried out to the Hessian matrixes of every bit, obtain three characteristic values and with three features
The one-to-one characteristic vector of value difference.
In the embodiment of the present invention, for Hessian matrix HsσThree characteristic values that (x, y, z) is obtained after being decomposed are designated as
λ1、λ2、λ3, and meet | λ1|≤|λ2|≤|λ3|；One-to-one three characteristic vectors are designated as respectively with three characteristic values
The characteristic value and characteristic vector of Hessian matrixes can describe the geometric properties of tubular structure.Specifically, for
The point belonged on tubular structure, its corresponding characteristic value of characteristic vector moved towards along blood vessel is less one in three characteristic values
It is individual；And along Zhang Chengyi plane of other two characteristic vector that vertical tangent plane direction is moved towards with blood vessel, and other two feature
The corresponding characteristic value size of vector is close, and is two larger in three characteristic values, that is, meets | λ3|≈|λ2| ＞ ＞ | λ1|≈
0。
S14：According to the characteristic value and characteristic vector of every bit, estimation corresponding points belong to tubular structure under each yardstick
Possibility.
Assuming that under yardstick σ, image midpoint (x, y, z) corresponding three characteristic values are met | λ1|≤|λ2|≤|λ3|, point (x,
Y, z) belong to the possibility of tubular structure for Vs(σ), then meet：
Wherein,Coeff is a constant, α be constant and
0 ＜ α ＜ 1, typically can use 0.5, β is constant and 0 ＜ β ＜ 1, typically can use the constant that 0.5, γ is setting.
S15：The maximum of possibility of the every bit under different scale is taken to belong to the possibility of tubular structure as corresponding points
The end value of property.
Assuming that the end value of the possibility is designated as V, then have：Wherein, σmin, σmaxIt is minimum respectively
Yardstick and out to out.
S2：It is big to other possibilities in its neighborhood using the minimum direction of the characteristic value of point of the possibility more than 0 as normal direction
In 0 point carry out rod Tensor Voting, and according to voting results to each possibility be more than 0 point characteristic value and characteristic vector enter
Line reconstruction, direction is moved towards to determine that each possibility is more than the tubular structure of 0 point.
Further, as shown in figure 3, step S2 may include following steps again：
S21：Using point of each possibility more than 0 as polling place, using the minimum direction of the characteristic value of correspondence polling place as normal
Other possibilities in its neighborhood are more than 0 point and carry out rod Tensor Voting for poll receiving point by direction.
Assuming that corresponding three characteristic values of point (x, y, z) that possibility is more than 0 are met | λ1|≤|λ2|≤|λ3|, feature to
Measure and beRod tensor is S, and plate tensor is P, and spheric tensor is B, then Hessian matrix of the point (x, y, z) under correspondence yardstick
Rod tensor, plate tensor sum spheric tensor sum are can be analyzed to for H, that is, is had：H=(λ3-λ2)S+(λ2-λ1)P+λ1B, wherein, (λ3-λ2) represent curved-surface display
Property.
In embodiments of the present invention, it is assumed that the point (x, y, z) that possibility is more than 0 is polling place, with point (x, y, z) feature
It is worth minimum directionFor normal direction, the point R that other possibilities in neighborhood are more than 0 is voted, R is poll receiving point,
The poll that then point (x, y, z) is launched to point R is the rod tensor Stick (l, θ, π) comprising direction and intensity, and is met：
Wherein,For conspicuousness attenuation function, andθ be point (x,
Y, z) with point R line l andThe angle for the plane opened,The normal direction of plane beS is line l
Arc length, σ specifies the range scale of ballot, determines the size of ballot window, c is range scale σ function, for restricting
The degree of degeneration of curvature, and meet：
In the embodiment of the present invention, by, for normal direction, being opened with minimal eigenvalue character pair vector plus a rod again
Measure conspicuousness (λ3-λ2) as weight, carry out rod Tensor Voting.After poll closing, each possibility in image is more than 0 all
The ballot that other points in surrounding neighbors can be obtained adds up.
S22：The characteristic value and characteristic vector for being more than 0 point to each possibility according to voting results are reconstructed, with true
What fixed each possibility was more than the tubular structure of 0 point moves towards direction.
In the embodiment of the present invention, the poll Stick (l, θ, π) received at poll receiving point R is added up, it is cumulative
Process includes the cumulative of tensor size and Orientation, remembers T 'R(x, y, z) is the cumulative tensor that receiving point is received, and spy is carried out to it
Levy decomposition：
Wherein | λ '3|≤|λ′2|≤|λ′1| it is T 'RThe characteristic value of (x, y, z),Opened to be added up after poll closing
Measure T 'RThe characteristic vector of (x, y, z), three new feature vector difference character pair values are minimum, secondary small, maximum characteristic value,
The direction of characteristic vector obtained by nowIt is the correction direction to artwork dispersal direction.
S3：According to the characteristic vector of reconstruct, the intensity for being more than 0 point to each possibility in image using spread function is entered
Row updates, untill update times reach maximum iteration.
In the embodiment of the present invention, the possibility of tubular structure in figure is diffused using VED algorithms, spread function is represented
For：Wherein, VtIt is the blood vessel intensity after diffusion, t is diffusion time,It is divergence operator, D is to expand
Tensor is dissipated, and is met：
Wherein,For the tensor T ' that added up after poll closing in the characteristic vector of reconstruct, i.e. step S22R(x, y, z)
Characteristic vector, ω be a parameter, the intensity to show anisotropy parameter, can use ω=5, ε be a parameter, to ensure
Diffusion tensor D is a positive definite matrix, and can use ε=0.01, L is a parameter, quick to control that spread function influences on blood vessel
Perception, can use L=2.
Fig. 4 shows the structure of the blood vessel strengthening system of lung CT image provided in an embodiment of the present invention, for the ease of saying
It is bright, the part related to the embodiment of the present invention is illustrate only, the system can be built in other all kinds of image transformation systems
Hardware cell, the combination of software unit or software and hardware unit.
Specifically, the blood vessel strengthening system of lung CT image provided in an embodiment of the present invention includes：Computing module 1, is used for
The Hessian matrixes and its characteristic value and characteristic vector of every bit in image are calculated, and is estimated according to characteristic value and characteristic vector
Every bit belongs to the possibility of tubular structure；Reconstructed module 2, for be more than using possibility the minimum direction of 0 characteristic value of point as
Normal direction, the point that 0 is more than to possibility in neighborhood carries out rod Tensor Voting, and each possibility is more than according to voting results
The characteristic value and characteristic vector of 0 point are reconstructed, to determine that each possibility is more than the side of trend of the tubular structure of 0 point
To；Module 3 is spread, for the characteristic vector according to reconstruct, 0 point is more than using spread function to each possibility in image
Intensity is updated, untill update times reach maximum iteration.
Further, as shown in figure 5, computing module 1 may include：Smooth submodule 11, for utilizing multiple dimensioned Gaussian function
It is several that image is carried out smoothly；First calculating sub module 12, under each yardstick, calculating each in image according to sharpening result
The Hessian matrixes of point；Second calculating sub module 13, carries out Eigenvalues Decomposition for the Hessian matrixes to every bit, obtains
Three characteristic values and distinguish one-to-one characteristic vectors with three characteristic values；Submodule 14 is estimated, for according to every bit
Characteristic value and characteristic vector, estimation every bit belongs to the possibility of tubular structure under each yardstick；Value submodule 15, is used
Belong to the end value of the possibility of tubular structure as every bit in the maximum for taking possibility of the every bit under different scale.
Wherein, described in the corresponding as above step S11 to S15 of the detailed execution flow of each submodule, do not repeat.
Further, as shown in fig. 6, reconstructed module 2 may include：Ballot submodule 21, for being more than 0 with each possibility
Point be polling place, to other possibilities be more than 0 point be poll receiving point carry out rod Tensor Voting；Submodule 22 is reconstructed, is used
The characteristic value and characteristic vector of the cumulative tensor received in the point for being more than 0 to each possibility according to voting results are reconstructed,
Direction is moved towards to determine that each possibility is more than the tubular structure of 0 point.Wherein, the detailed execution flow pair of each submodule
Answer described in as above step S21 to S22, do not repeat.
In summary, the blood vessel Enhancement Method and system for the lung CT image that the embodiment of the present invention is proposed are to VED algorithms
Improved, estimated after every bit belongs to the possibility of tubular structure, by rod Tensor Voting, to characteristic value and spy
Levy vector to be reconstructed, recycle spread function to carry out image enhaucament afterwards.Relative to VED algorithms, due to make use of neighborhood
Tensor direction, rod Tensor Voting has been carried out to the blood vessel of vascular wall trend, so as to correct for the tensor direction around vascular wall
And new tensor direction is reconstructed, it can preferably reduce expansion of the blood vessel intensity along blood vessel tangent plane using the tensor direction of reconstruct
Dissipate, while diffusion of the enhancing along vessel directions, reaches suppression noise, strengthen the effect of blood vessel feature, solve the presence of VED algorithms
Tubular structure edge feature direction it is mixed and disorderly caused by enhancing effect distortion the problem of.
Can be with one of ordinary skill in the art will appreciate that realizing that all or part of step in above-described embodiment method is
Control the hardware of correlation to complete by program, described program can in a computer read/write memory medium is stored in,
Described storage medium, such as ROM/RAM, disk, CD.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all essences in the present invention
Any modifications, equivalent substitutions and improvements made within refreshing and principle etc., should be included in the scope of the protection.
Claims (7)
1. the blood vessel Enhancement Method of a kind of lung CT image, it is characterised in that the described method comprises the following steps：
The Hessian matrixes and its characteristic value and characteristic vector of every bit in image are calculated, and according to characteristic value and characteristic vector
Estimation every bit belongs to the possibility of tubular structure；
Using the minimum direction of the characteristic value of point of the possibility more than 0 as normal direction, 0 click-through is more than to other possibilities in neighborhood
Row rod Tensor Voting, and according to voting results to each possibility be more than 0 point characteristic value and characteristic vector be reconstructed, with
Determine that each possibility is more than the tubular structure of 0 point and moves towards direction；
According to the characteristic vector of reconstruct, it is more than the intensity of 0 point to each possibility described in described image using spread function
It is updated, untill update times reach maximum iteration；
Wherein, the minimum direction of the characteristic value of the point that 0 is more than using possibility is big to other possibilities in neighborhood as normal direction
Comprise the following steps the step of 0 point carries out rod Tensor Voting：
Using point of each possibility more than 0 as polling place, using the minimum direction of the characteristic value of correspondence polling place as normal direction, with
It is poll receiving point progress rod Tensor Voting that other possibilities, which are more than 0 point, in neighborhood；
Wherein, the poll Stick (l, θ, π) received at poll receiving point R is added up, it is big that cumulative process includes tensor
Cumulative, the note T ' in small and directionR(x, y, z) is the cumulative tensor that the poll receiving point R is received, and the cumulative tensor is entered
Row feature decomposition：
Wherein λ '3, λ '2, λ '1For T 'RThe characteristic value of (x, y, z), and | λ '3|≤|λ′2|≤|λ′1|,For poll closing
The cumulative tensor T ' afterwardsRThe characteristic vector of (x, y, z), that is, the characteristic vector after reconstructing, wherein eigenvalue of maximum λ '1It is corresponding
Characteristic vectorDirection be dispersal direction.
2. the blood vessel Enhancement Method of lung CT image as claimed in claim 1, it is characterised in that each in the calculating image
The Hessian matrixes and its characteristic value and characteristic vector of point, and tubulose is belonged to according to characteristic value and characteristic vector estimation every bit
The step of possibility of structure, comprises the following steps：
Image is carried out using multiple dimensioned Gaussian function smooth；
Under each yardstick, the Hessian matrixes of every bit in image are calculated according to sharpening result；
Eigenvalues Decomposition is carried out to the Hessian matrixes of the every bit, three characteristic values is obtained and divides with three characteristic values
Not one-to-one characteristic vector；
According to the characteristic value and characteristic vector of every bit, estimation every bit belongs to the possibility of tubular structure under each yardstick；
Take possibility of the every bit under different scale maximum belong to as every bit tubular structure possibility it is final
Value.
3. the blood vessel Enhancement Method of lung CT image as claimed in claim 2, it is characterised in that if yardstick is high for σ three-dimensional
This function is G (x, y, z；σ), described image is I (x, y, z), and described image is smooth knots of the I (x, y, z) under the yardstick σ
Fruit is Iσ(x, y, z), then it is described that smooth be expressed as is carried out to image using multiple dimensioned Gaussian function：Wherein,
If under the yardstick σ, the Hessian matrixes at described image midpoint (x, y, z) place are Hσ(x, y, z), then it is described in each chi
Under degree, it is expressed as according to the Hessian matrixes that sharpening result calculates every bit in image：
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</mrow>
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<mo>&part;</mo>
<mi>y</mi>
<mo>&part;</mo>
<mi>z</mi>
</mrow>
</mfrac>
</mtd>
<mtd>
<mfrac>
<mrow>
<mo>&part;</mo>
<msubsup>
<mi>I</mi>
<mi>&alpha;</mi>
<mn>2</mn>
</msubsup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo>,</mo>
<mi>z</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mo>&part;</mo>
<msup>
<mi>z</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>;</mo>
</mrow>
If under the yardstick σ, described image midpoint (x, y, z) corresponding three characteristic values are λ1、λ2、λ3, and meet | λ1|≤|λ2
|≤|λ3|, the possibility that the point (x, y, z) belongs to tubular structure is Vs(σ), the then characteristic value and spy according to every bit
Vector is levied, estimation every bit belongs to being expressed as the possibility of tubular structure under each yardstick：
<mrow>
<msub>
<mi>V</mi>
<mi>s</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>&sigma;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
<mo>></mo>
<mn>0</mn>
<msub>
<mi>or&lambda;</mi>
<mn>3</mn>
</msub>
<mo>></mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<mfrac>
<msubsup>
<mi>R</mi>
<mi>A</mi>
<mn>2</mn>
</msubsup>
<mrow>
<mn>2</mn>
<msup>
<mi>&alpha;</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
</mrow>
</msup>
<mo>)</mo>
<mo>&CenterDot;</mo>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<mfrac>
<msubsup>
<mi>R</mi>
<mi>B</mi>
<mn>2</mn>
</msubsup>
<mrow>
<mn>2</mn>
<msup>
<mi>&beta;</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
</mrow>
</msup>
<mo>&CenterDot;</mo>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<mfrac>
<msup>
<mi>S</mi>
<mn>2</mn>
</msup>
<mrow>
<mn>2</mn>
<msup>
<mi>&gamma;</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
</mrow>
</msup>
<mo>)</mo>
<mo>&CenterDot;</mo>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<mfrac>
<mrow>
<mn>2</mn>
<msup>
<mi>Coeff</mi>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mo>|</mo>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
<mo>|</mo>
<msubsup>
<mi>&lambda;</mi>
<mn>3</mn>
<mn>2</mn>
</msubsup>
</mrow>
</mfrac>
</mrow>
</msup>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>o</mi>
<mi>t</mi>
<mi>h</mi>
<mi>e</mi>
<mi>r</mi>
<mi>w</mi>
<mi>i</mi>
<mi>s</mi>
<mi>e</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Wherein,Coeff is a constant, and α is constant and 0 ＜ α ＜
1, β is constant and 0 ＜ β ＜ 1, γ are the constants of setting；
Take possibility of the every bit under different scale maximum belong to as every bit tubular structure possibility it is final
Value, it is assumed that the end value of the possibility is designated as V, then has：Wherein, σmin, σmaxIt is minimum chi respectively
Degree and out to out.
4. the blood vessel Enhancement Method of lung CT image as claimed in claim 1, it is characterised in that if possibility in described image
Corresponding three characteristic values of point (x, y, z) more than 0 are λ1、λ2、λ3, and meet | λ1|≤|λ2|≤|λ3|, corresponding feature to
Measure and beWith the minimum direction of the characteristic value of the point (x, y, z) for normal direction, possibility is more than 0 in its neighborhood
Point R is poll receiving point, then the poll that the point (x, y, z) is launched to the point R is the rod tensor comprising direction and intensity
Stick (l, θ, π), and meet：
<mrow>
<mi>S</mi>
<mi>t</mi>
<mi>i</mi>
<mi>c</mi>
<mi>k</mi>
<mrow>
<mo>(</mo>
<mi>l</mi>
<mo>,</mo>
<mi>&theta;</mi>
<mo>,</mo>
<mi>&pi;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>&lambda;</mi>
<mn>3</mn>
</msub>
<mo>-</mo>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
<mi>D</mi>
<mi>F</mi>
<mrow>
<mo>(</mo>
<mi>s</mi>
<mo>,</mo>
<mi>k</mi>
<mo>,</mo>
<mi>&sigma;</mi>
<mo>)</mo>
</mrow>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mo>-</mo>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<mo>(</mo>
<mn>2</mn>
<mi>&theta;</mi>
<mo>)</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>cos</mi>
<mo>(</mo>
<mn>2</mn>
<mi>&theta;</mi>
<mo>)</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Wherein,For conspicuousness attenuation function, andθ is point (x, y, z)
With point R line l withThe angle for the plane opened, s is line l arc length, and σ specifies the range scale of ballot, is determined
The size of ballot window, c is range scale σ function, and is met：
5. the blood vessel Enhancement Method of lung CT image as claimed in claim 1, it is characterised in that the spread function isWherein, VtIt is the blood vessel intensity after diffusion, t is diffusion time,It is divergence operator, V is the figure
Picture midpoint (x, y, z) belongs to the possibility of tubular structure, and D is diffusion tensor, and meets：
<mrow>
<msubsup>
<mi>&lambda;</mi>
<mn>1</mn>
<mrow>
<mo>&prime;</mo>
<mo>&prime;</mo>
</mrow>
</msubsup>
<mo>=</mo>
<mn>1</mn>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mi>&omega;</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<msup>
<mi>V</mi>
<mfrac>
<mn>1</mn>
<mi>L</mi>
</mfrac>
</msup>
</mrow>
<mrow>
<msubsup>
<mi>&lambda;</mi>
<mn>2</mn>
<mrow>
<mo>&prime;</mo>
<mo>&prime;</mo>
</mrow>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>&lambda;</mi>
<mn>3</mn>
<mrow>
<mo>&prime;</mo>
<mo>&prime;</mo>
</mrow>
</msubsup>
<mo>=</mo>
<mn>1</mn>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mi>&epsiv;</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<msup>
<mi>V</mi>
<mfrac>
<mn>1</mn>
<mi>L</mi>
</mfrac>
</msup>
</mrow>
Wherein,For the characteristic vector of reconstruct, ω is a parameter, the intensity to show anisotropy parameter；ε is one
Parameter, to ensure that diffusion tensor D is a positive definite matrix, ω is more than ε；L is a parameter, to control spread function to blood vessel
The sensitiveness of influence.
6. the blood vessel strengthening system of a kind of lung CT image, it is characterised in that the system includes：
Computing module, Hessian matrixes and its characteristic value and characteristic vector for calculating every bit in image, and according to feature
Value and characteristic vector estimation every bit belong to the possibility of tubular structure；
Reconstructed module, for being more than the minimum direction of 0 characteristic value of point using possibility as normal direction, to other possibility in neighborhood
Property be more than 0 point carry out rod Tensor Voting, and according to voting results to each possibility be more than 0 point characteristic value and feature to
Amount is reconstructed, and direction is moved towards to determine that each possibility is more than the tubular structure of 0 point；
Module is spread, for the characteristic vector according to reconstruct, 0 is more than to each possibility described in image using spread function
The intensity of point is updated, untill update times reach maximum iteration；
Wherein, the reconstructed module includes：
Ballot submodule, for using point of each possibility more than 0 as polling place, with the minimum direction of the characteristic value of correspondence polling place
For normal direction, point of other possibilities more than 0 carries out rod Tensor Voting as poll receiving point using in neighborhood；
Submodule is reconstructed, the characteristic value and characteristic vector for the point according to voting results to each possibility more than 0 are entered
Line reconstruction, direction is moved towards to determine that each possibility is more than the tubular structure of 0 point；
Wherein, the poll Stick (l, θ, π) received at poll receiving point R is added up, it is big that cumulative process includes tensor
Cumulative, the note T ' in small and directionR(x, y, z) is the cumulative tensor that the poll receiving point R is received, and the cumulative tensor is entered
Row feature decomposition：
Wherein λ '3, λ '2, λ '1For T 'RThe characteristic value of (x, y, z), and | λ '3|≤|λ′2|≤|λ′1|,For poll closing
The cumulative tensor T ' afterwardsRThe characteristic vector of (x, y, z), that is, the characteristic vector after reconstructing, wherein eigenvalue of maximum λ '1It is corresponding
Characteristic vectorDirection is dispersal direction.
7. the blood vessel strengthening system of lung CT image as claimed in claim 6, it is characterised in that the computing module includes：
Smooth submodule, it is smooth for being carried out using multiple dimensioned Gaussian function to image；
First calculating sub module, under each yardstick, the Hessian squares of every bit in image to be calculated according to sharpening result
Battle array；
Second calculating sub module, carries out Eigenvalues Decomposition for the Hessian matrixes to the every bit, obtains three characteristic values
And distinguish one-to-one characteristic vector with three characteristic values；
Submodule is estimated, for the characteristic value and characteristic vector according to every bit, estimation every bit belongs to pipe under each yardstick
The possibility of shape structure；
Value submodule, belongs to tubular structure for taking the maximum of possibility of the every bit under different scale as every bit
Possibility end value.
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| CN101116103A (en) * | 2005-02-11 | 2008-01-30 | 皇家飞利浦电子股份有限公司 | Method of automatic extraction of the pulmonary artery tree from 3d medical images |
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